This document contains visualisation and analysis of data in Pak choi pollinators raw visits Brad correctedupdatedHeatherxlsx (002).xlsx which was previously cleaned.
This analysis was performed using R version 4.4.1 (2024-06-14 ucrt). The tidyverse suite of packages was used for data manipulation and visualisation. The emmeans package was used for model predictions.
How does the presence and age of native SNH influence pollinator diversity (species richness and evenness and seed yield on exotic crop plants compared to bare fence lines on farms with the SNH (distance >400m from SNH) and bare-fence-lines on farms without SNH?
Does farm type influence pollinator abundance and species composition and resulting seed yields?
Does visitation differ between exotic or native species, or between bees and flies in relation to farm type or the presence of native plantings? Does this influence seed yield?
The cleaned data is loaded.
## tibble [5,865 × 11] (S3: tbl_df/tbl/data.frame)
## $ farm_type : Factor w/ 2 levels "Arable","Dairy": 1 1 1 1 1 1 1 1 1 1 ...
## $ farm_name : Factor w/ 19 levels "Ahuriri","Ashford_1",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ season : Factor w/ 3 levels "2021/22","2022/23",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ boundary_descriptor : Factor w/ 6 levels "Control farm",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ boundary_age : num [1:5865] NA NA NA NA NA NA NA NA NA NA ...
## $ insect_key_number : Factor w/ 51 levels "1","2","3","4",..: 1 2 3 4 5 6 7 8 9 10 ...
## $ new_insect_key_name : Factor w/ 51 levels "Black bulb hover fly",..: 20 6 33 23 2 30 21 22 39 50 ...
## $ sum_of_insects_100_flowers: num [1:5865] 2.58 0 0 0 0 ...
## $ broad_insect_category : Factor w/ 3 levels "Honey bees","Non-bees",..: 1 3 3 3 3 3 3 2 2 2 ...
## $ origin : Factor w/ 3 levels "Native","Both",..: 3 3 3 1 3 1 1 3 2 3 ...
## $ boundary_alt : Factor w/ 4 levels "Control farm",..: 1 1 1 1 1 1 1 1 1 1 ...
The data is summarised by taking the means for each insect, ignoring the treatments etc so we can get a feel for the numbers for each of the 51 insects.
| new_insect_key_name | broad_insect_category | origin | Mean_count_per_100_flowers |
|---|---|---|---|
| Lasioglossum bee | Wild bees | Native | 7.378 |
| Drone fly | Non-bees | Exotic | 5.054 |
| NZ orange hover fly | Non-bees | Native | 4.866 |
| Striped flesh fly | Non-bees | Exotic | 1.586 |
| NZ black hover fly | Non-bees | Native | 0.987 |
| Honey bee | Honey bees | Exotic | 0.971 |
| Seedcorn maggot fly | Non-bees | Exotic | 0.870 |
| Buff-tailed bumble bee | Wild bees | Exotic | 0.621 |
| Pollenia flies | Non-bees | Native | 0.620 |
| Other insects | Non-bees | Both | 0.571 |
| Ichneumonid wasps | Non-bees | Exotic | 0.498 |
| Bronze cluster flies | Non-bees | Exotic | 0.469 |
| Cabbage white butterfly | Non-bees | Exotic | 0.436 |
| Hylaeus bees | Wild bees | Native | 0.241 |
| Eleven spotted ladybird | Non-bees | Exotic | 0.148 |
| Other muscid flies | Non-bees | Both | 0.113 |
| European blue blow fly | Non-bees | Exotic | 0.101 |
| NZ blue hover fly | Non-bees | Native | 0.098 |
| Other parasitoid wasps | Non-bees | Both | 0.097 |
| Yellow admiral butterfly | Non-bees | Native | 0.091 |
| Other moths | Non-bees | Both | 0.085 |
| Globetail hover fly | Non-bees | Exotic | 0.068 |
| Grey triangle muscid fly | Non-bees | Native | 0.064 |
| Brown blow fly | Non-bees | Exotic | 0.060 |
| Streaktail hover fly | Non-bees | Native | 0.059 |
| European green blow fly | Non-bees | Exotic | 0.055 |
| Black Leioproctus bees | Wild bees | Exotic | 0.051 |
| Orange Leioproctus bee | Wild bees | Native | 0.045 |
| Magpie moth | Non-bees | Exotic | 0.045 |
| Small ginger blister fly | Non-bees | Exotic | 0.042 |
| Green soldier fly | Non-bees | Native | 0.036 |
| Black bulb hover fly | Non-bees | Exotic | 0.034 |
| Ginger blister fly | Non-bees | Native | 0.031 |
| Red admiral butterfly | Non-bees | Native | 0.030 |
| Three spotted fly | Non-bees | Exotic | 0.025 |
| Grey-black bristle flies | Non-bees | Native | 0.025 |
| Other hover flies | Non-bees | Both | 0.023 |
| Other wasps | Non-bees | Both | 0.022 |
| Common copper butterfly | Non-bees | Native | 0.022 |
| Other bristle flies | Non-bees | Both | 0.016 |
| Other bumblebees | Wild bees | Exotic | 0.016 |
| European tube wasp | Non-bees | Exotic | 0.015 |
| Blue muscid fly | Non-bees | Exotic | 0.014 |
| Other blow flies | Non-bees | Exotic | 0.011 |
| Flower longhorn beetle | Non-bees | Native | 0.008 |
| Scaptia horse flies | Non-bees | Native | 0.006 |
| NZ blue blow fly | Non-bees | Native | 0.006 |
| Other ladybirds | Non-bees | Exotic | 0.005 |
| Vespula wasps | Non-bees | Exotic | 0.004 |
| March fly | Non-bees | Native | 0.004 |
| Spotted hover fly | Non-bees | Native | 0.004 |
The data is grouped by the broad insect category and the counts are summed, then the mean across the farm type, season and boundary descriptor is taken. These numbers are graphed.
The data is grouped by the origin category and the counts are summed, then the mean across the farm type, season and boundary descriptor is taken. These numbers are graphed.
The new boundary descriptor has the “1-3 year old” categories. collapsed into single category called New. Most of the time “One year old” is in 2021/22, “Two year old” is in 2022/23 and “Three year old” is in 2023/24.
In the first graph below, observations from the same farm are joined by a line.
In the first graph below, observations from the same farm are joined by a line.
We remove the six observations where 2023/24 is One/Two year old. This means that the category “new” just has
(If we don’t want to interpret anything to do with how “new” the plantings are, we can include this data. Let me know if this is the case.)
The raw means are given below
| farm_type | boundary_alt | season | broad_insect_category | mean | n |
|---|---|---|---|---|---|
| Arable | Control farm | 2021/22 | Honey bees | 1.49 | 2 |
| Arable | Control farm | 2021/22 | Non-bees | 13.49 | 2 |
| Arable | Control farm | 2021/22 | Wild bees | 2.02 | 2 |
| Arable | Control farm | 2022/23 | Honey bees | 0.83 | 2 |
| Arable | Control farm | 2022/23 | Non-bees | 2.52 | 2 |
| Arable | Control farm | 2022/23 | Wild bees | 1.51 | 2 |
| Arable | Control farm | 2023/24 | Honey bees | 0.31 | 5 |
| Arable | Control farm | 2023/24 | Non-bees | 10.70 | 5 |
| Arable | Control farm | 2023/24 | Wild bees | 2.88 | 5 |
| Arable | Bare fence | 2021/22 | Honey bees | 0.35 | 3 |
| Arable | Bare fence | 2021/22 | Non-bees | 21.34 | 3 |
| Arable | Bare fence | 2021/22 | Wild bees | 0.94 | 3 |
| Arable | Bare fence | 2022/23 | Honey bees | 0.33 | 3 |
| Arable | Bare fence | 2022/23 | Non-bees | 9.69 | 3 |
| Arable | Bare fence | 2022/23 | Wild bees | 3.96 | 3 |
| Arable | Bare fence | 2023/24 | Honey bees | 0.92 | 4 |
| Arable | Bare fence | 2023/24 | Non-bees | 7.45 | 4 |
| Arable | Bare fence | 2023/24 | Wild bees | 6.33 | 4 |
| Arable | Old | 2021/22 | Honey bees | 1.00 | 4 |
| Arable | Old | 2021/22 | Non-bees | 27.76 | 4 |
| Arable | Old | 2021/22 | Wild bees | 4.27 | 4 |
| Arable | Old | 2022/23 | Honey bees | 1.86 | 4 |
| Arable | Old | 2022/23 | Non-bees | 14.73 | 4 |
| Arable | Old | 2022/23 | Wild bees | 5.73 | 4 |
| Arable | Old | 2023/24 | Honey bees | 4.22 | 5 |
| Arable | Old | 2023/24 | Non-bees | 19.77 | 5 |
| Arable | Old | 2023/24 | Wild bees | 10.16 | 5 |
| Arable | New | 2021/22 | Honey bees | 0.50 | 3 |
| Arable | New | 2021/22 | Non-bees | 21.23 | 3 |
| Arable | New | 2021/22 | Wild bees | 2.84 | 3 |
| Arable | New | 2022/23 | Honey bees | 1.91 | 4 |
| Arable | New | 2022/23 | Non-bees | 12.39 | 4 |
| Arable | New | 2022/23 | Wild bees | 7.19 | 4 |
| Arable | New | 2023/24 | Honey bees | 2.65 | 4 |
| Arable | New | 2023/24 | Non-bees | 29.17 | 4 |
| Arable | New | 2023/24 | Wild bees | 12.14 | 4 |
| Dairy | Control farm | 2021/22 | Honey bees | 0.00 | 7 |
| Dairy | Control farm | 2021/22 | Non-bees | 28.00 | 7 |
| Dairy | Control farm | 2021/22 | Wild bees | 5.14 | 7 |
| Dairy | Control farm | 2022/23 | Honey bees | 0.07 | 7 |
| Dairy | Control farm | 2022/23 | Non-bees | 7.53 | 7 |
| Dairy | Control farm | 2022/23 | Wild bees | 1.72 | 7 |
| Dairy | Control farm | 2023/24 | Honey bees | 0.04 | 6 |
| Dairy | Control farm | 2023/24 | Non-bees | 13.26 | 6 |
| Dairy | Control farm | 2023/24 | Wild bees | 2.10 | 6 |
| Dairy | Bare fence | 2021/22 | Honey bees | 0.38 | 7 |
| Dairy | Bare fence | 2021/22 | Non-bees | 19.81 | 7 |
| Dairy | Bare fence | 2021/22 | Wild bees | 6.35 | 7 |
| Dairy | Bare fence | 2022/23 | Honey bees | 0.35 | 7 |
| Dairy | Bare fence | 2022/23 | Non-bees | 4.92 | 7 |
| Dairy | Bare fence | 2022/23 | Wild bees | 0.53 | 7 |
| Dairy | Bare fence | 2023/24 | Honey bees | 2.06 | 3 |
| Dairy | Bare fence | 2023/24 | Non-bees | 9.46 | 3 |
| Dairy | Bare fence | 2023/24 | Wild bees | 2.05 | 3 |
| Dairy | Old | 2021/22 | Honey bees | 0.71 | 8 |
| Dairy | Old | 2021/22 | Non-bees | 25.17 | 8 |
| Dairy | Old | 2021/22 | Wild bees | 20.70 | 8 |
| Dairy | Old | 2022/23 | Honey bees | 0.92 | 8 |
| Dairy | Old | 2022/23 | Non-bees | 8.48 | 8 |
| Dairy | Old | 2022/23 | Wild bees | 17.21 | 8 |
| Dairy | Old | 2023/24 | Honey bees | 0.94 | 8 |
| Dairy | Old | 2023/24 | Non-bees | 24.26 | 8 |
| Dairy | Old | 2023/24 | Wild bees | 22.34 | 8 |
| Dairy | New | 2021/22 | Honey bees | 1.29 | 3 |
| Dairy | New | 2021/22 | Non-bees | 46.42 | 3 |
| Dairy | New | 2021/22 | Wild bees | 13.01 | 3 |
| Dairy | New | 2022/23 | Honey bees | 0.07 | 3 |
| Dairy | New | 2022/23 | Non-bees | 11.16 | 3 |
| Dairy | New | 2022/23 | Wild bees | 4.29 | 3 |
| Dairy | New | 2023/24 | Honey bees | 1.52 | 3 |
| Dairy | New | 2023/24 | Non-bees | 28.82 | 3 |
| Dairy | New | 2023/24 | Wild bees | 18.09 | 3 |
It is not possible to model the variability of the combination
Dairy, Control farm, 2021/22, Honey bees
because it has a mean of zero. This data is removed from the model.
We fit a zero-inflated negative binomial generalised linear mixed model. The log link function is used. The zero-inflated part of the model has just an intercept, the zero-inflation is the same for all the fixed-effect combinations. There is also a term in the model to account for over dispersion. The AIC was used to select that.
The GLMM part of the model has the four-way interaction of farm_type, broad_insect_category, boundary_alt and season There is a random effect for boundary_alt:farm_name.
The ANOVA table is
| Chisq | Df | Pr(>Chisq) | |
|---|---|---|---|
| farm_type | 0.046 | 1 | 0.831 |
| broad_insect_category | 349.748 | 2 | 0.000 |
| boundary_alt | 47.376 | 3 | 0.000 |
| season | 81.309 | 2 | 0.000 |
| farm_type:broad_insect_category | 7.952 | 2 | 0.019 |
| farm_type:boundary_alt | 2.942 | 3 | 0.401 |
| broad_insect_category:boundary_alt | 34.891 | 6 | 0.000 |
| farm_type:season | 11.163 | 2 | 0.004 |
| broad_insect_category:season | 12.852 | 4 | 0.012 |
| boundary_alt:season | 9.856 | 6 | 0.131 |
| farm_type:broad_insect_category:boundary_alt | 23.814 | 6 | 0.001 |
| farm_type:broad_insect_category:season | 8.550 | 4 | 0.073 |
| farm_type:boundary_alt:season | 6.960 | 6 | 0.325 |
| broad_insect_category:boundary_alt:season | 11.935 | 12 | 0.451 |
| farm_type:broad_insect_category:boundary_alt:season | 11.004 | 11 | 0.443 |
Thankfully, the four-way interaction is not significant. We have one three-way interaction to consider
and two two-way interactions (with season in which is missing from the three-way)
The data is grouped by the broad insect category and the number of different insects with non-zero counts is calculated. These numbers are graphed. The honey bees and wild bees and put together.
We fit a negative binomial generalised linear mixed model. The log link function is used.
The GLMM part of the model has main effects for farm_type, broad_insect_category2, boundary_alt and season. There is a random effect for boundary_alt:farm_name.
The model did not converge with the four-way interaction, and the AIC was better with just main effects.
The ANOVA table is:
| Chisq | Df | Pr(>Chisq) | |
|---|---|---|---|
| farm_type | 0.047 | 1 | 0.828 |
| boundary_alt | 52.917 | 3 | 0.000 |
| season | 22.583 | 2 | 0.000 |
| broad_insect_category2 | 245.406 | 1 | 0.000 |
farm_type is not significant, but the other three factors are.
The raw means are given below
| farm_type | boundary_alt | season | origin | mean | n |
|---|---|---|---|---|---|
| Arable | Control farm | 2021/22 | Native | 9.70 | 2 |
| Arable | Control farm | 2021/22 | Both | 0.99 | 2 |
| Arable | Control farm | 2021/22 | Exotic | 6.32 | 2 |
| Arable | Control farm | 2022/23 | Native | 1.40 | 2 |
| Arable | Control farm | 2022/23 | Both | 0.00 | 2 |
| Arable | Control farm | 2022/23 | Exotic | 3.46 | 2 |
| Arable | Control farm | 2023/24 | Native | 6.15 | 5 |
| Arable | Control farm | 2023/24 | Both | 0.24 | 5 |
| Arable | Control farm | 2023/24 | Exotic | 7.49 | 5 |
| Arable | Bare fence | 2021/22 | Native | 7.95 | 3 |
| Arable | Bare fence | 2021/22 | Both | 0.00 | 3 |
| Arable | Bare fence | 2021/22 | Exotic | 14.68 | 3 |
| Arable | Bare fence | 2022/23 | Native | 8.11 | 3 |
| Arable | Bare fence | 2022/23 | Both | 0.41 | 3 |
| Arable | Bare fence | 2022/23 | Exotic | 5.45 | 3 |
| Arable | Bare fence | 2023/24 | Native | 7.91 | 4 |
| Arable | Bare fence | 2023/24 | Both | 0.19 | 4 |
| Arable | Bare fence | 2023/24 | Exotic | 6.61 | 4 |
| Arable | Old | 2021/22 | Native | 19.38 | 4 |
| Arable | Old | 2021/22 | Both | 0.14 | 4 |
| Arable | Old | 2021/22 | Exotic | 13.51 | 4 |
| Arable | Old | 2022/23 | Native | 10.94 | 4 |
| Arable | Old | 2022/23 | Both | 0.17 | 4 |
| Arable | Old | 2022/23 | Exotic | 11.21 | 4 |
| Arable | Old | 2023/24 | Native | 16.27 | 5 |
| Arable | Old | 2023/24 | Both | 1.77 | 5 |
| Arable | Old | 2023/24 | Exotic | 16.10 | 5 |
| Arable | New | 2021/22 | Native | 10.30 | 3 |
| Arable | New | 2021/22 | Both | 0.38 | 3 |
| Arable | New | 2021/22 | Exotic | 13.89 | 3 |
| Arable | New | 2022/23 | Native | 11.79 | 4 |
| Arable | New | 2022/23 | Both | 0.49 | 4 |
| Arable | New | 2022/23 | Exotic | 9.21 | 4 |
| Arable | New | 2023/24 | Native | 16.89 | 4 |
| Arable | New | 2023/24 | Both | 2.91 | 4 |
| Arable | New | 2023/24 | Exotic | 24.17 | 4 |
| Dairy | Control farm | 2021/22 | Native | 15.66 | 7 |
| Dairy | Control farm | 2021/22 | Both | 0.28 | 7 |
| Dairy | Control farm | 2021/22 | Exotic | 17.21 | 7 |
| Dairy | Control farm | 2022/23 | Native | 3.92 | 7 |
| Dairy | Control farm | 2022/23 | Both | 0.90 | 7 |
| Dairy | Control farm | 2022/23 | Exotic | 4.49 | 7 |
| Dairy | Control farm | 2023/24 | Native | 6.78 | 6 |
| Dairy | Control farm | 2023/24 | Both | 1.49 | 6 |
| Dairy | Control farm | 2023/24 | Exotic | 7.13 | 6 |
| Dairy | Bare fence | 2021/22 | Native | 14.52 | 7 |
| Dairy | Bare fence | 2021/22 | Both | 0.19 | 7 |
| Dairy | Bare fence | 2021/22 | Exotic | 11.82 | 7 |
| Dairy | Bare fence | 2022/23 | Native | 2.49 | 7 |
| Dairy | Bare fence | 2022/23 | Both | 0.21 | 7 |
| Dairy | Bare fence | 2022/23 | Exotic | 3.09 | 7 |
| Dairy | Bare fence | 2023/24 | Native | 4.08 | 3 |
| Dairy | Bare fence | 2023/24 | Both | 0.35 | 3 |
| Dairy | Bare fence | 2023/24 | Exotic | 9.15 | 3 |
| Dairy | Old | 2021/22 | Native | 28.92 | 8 |
| Dairy | Old | 2021/22 | Both | 0.35 | 8 |
| Dairy | Old | 2021/22 | Exotic | 17.31 | 8 |
| Dairy | Old | 2022/23 | Native | 21.09 | 8 |
| Dairy | Old | 2022/23 | Both | 0.29 | 8 |
| Dairy | Old | 2022/23 | Exotic | 5.23 | 8 |
| Dairy | Old | 2023/24 | Native | 27.65 | 8 |
| Dairy | Old | 2023/24 | Both | 4.00 | 8 |
| Dairy | Old | 2023/24 | Exotic | 15.89 | 8 |
| Dairy | New | 2021/22 | Native | 50.56 | 3 |
| Dairy | New | 2021/22 | Both | 0.53 | 3 |
| Dairy | New | 2021/22 | Exotic | 9.64 | 3 |
| Dairy | New | 2022/23 | Native | 7.26 | 3 |
| Dairy | New | 2022/23 | Both | 2.32 | 3 |
| Dairy | New | 2022/23 | Exotic | 5.94 | 3 |
| Dairy | New | 2023/24 | Native | 23.70 | 3 |
| Dairy | New | 2023/24 | Both | 1.99 | 3 |
| Dairy | New | 2023/24 | Exotic | 22.74 | 3 |
It is not possible to model the variability of the combinations
because the data has a mean of zero. We remove all the “Both” data from the model.
We fit a negative binomial generalised linear mixed model. The log link function is used. The model has the four-way interaction of farm_type, origin, boundary_alt and season. There is a random effect for boundary_alt:farm_name.
The ANOVA table is
| Chisq | Df | Pr(>Chisq) | |
|---|---|---|---|
| farm_type | 0.424 | 1 | 0.515 |
| origin | 6.347 | 1 | 0.012 |
| boundary_alt | 49.261 | 3 | 0.000 |
| season | 75.967 | 2 | 0.000 |
| farm_type:origin | 4.566 | 1 | 0.033 |
| farm_type:boundary_alt | 3.441 | 3 | 0.328 |
| origin:boundary_alt | 14.221 | 3 | 0.003 |
| farm_type:season | 7.818 | 2 | 0.020 |
| origin:season | 2.149 | 2 | 0.341 |
| boundary_alt:season | 15.799 | 6 | 0.015 |
| farm_type:origin:boundary_alt | 4.772 | 3 | 0.189 |
| farm_type:origin:season | 1.455 | 2 | 0.483 |
| farm_type:boundary_alt:season | 4.511 | 6 | 0.608 |
| origin:boundary_alt:season | 4.090 | 6 | 0.665 |
| farm_type:origin:boundary_alt:season | 12.056 | 6 | 0.061 |
The four-way interaction is not significant. None of the three-way interactions are significant. We have four two-way interactions to consider
The data is grouped by the origin insect category and the number of different insects with non-zero counts is calculated. We remove the “both” category because there too many zeros for modelling.
We fit a negative binomial generalised linear mixed model. The log link function is used.
The model has main effects for farm_type, broad_insect_category2, boundary_alt and season plus the two-way interaction between farm_type and season. There is a random effect for boundary_alt:farm_name.
The model has a parameterised dispersion structure using season.
The model did not converge with additional terms.
The ANOVA table is:
| Chisq | Df | Pr(>Chisq) | |
|---|---|---|---|
| farm_type | 0.003 | 1 | 0.953 |
| season | 23.994 | 2 | 0.000 |
| boundary_alt | 50.457 | 3 | 0.000 |
| origin | 12.731 | 1 | 0.000 |
| farm_type:season | 8.656 | 2 | 0.013 |
The two-way interaction farm_type: season is significant, as are the main effects for origin and boundary_alt.
The following were more abundant on average than honey bees: Drone fly, Lasioglossum bee, NZ black hover fly, NZ orange hover fly, Striped flesh fly.
In the five models below zero-inflation and dispersion were considered when fitting the models. The AIC and BIC were looked at in conjunction with simulateResiduals and other functions from the DHARMa package were used. In each case the model was “better” (or no worse) without additional terms.
We fit a negative binomial generalised linear mixed model. The log link function is used. The model has the three-way interaction of farm_type, boundary_alt and season. There is a random effect for boundary_alt:farm_name.
The ANOVA table is
| Chisq | Df | Pr(>Chisq) | |
|---|---|---|---|
| farm_type | 4.095 | 1 | 0.043 |
| boundary_alt | 51.212 | 3 | 0.000 |
| season | 4.612 | 2 | 0.100 |
| farm_type:boundary_alt | 9.105 | 3 | 0.028 |
| farm_type:season | 14.775 | 2 | 0.001 |
| boundary_alt:season | 4.746 | 6 | 0.577 |
| farm_type:boundary_alt:season | 9.001 | 6 | 0.174 |
There are two two-way interactions to consider
We fit a negative binomial generalised linear mixed model. The log link function is used. The model has the three-way interaction of farm_type, boundary_alt and season. There is a random effect for boundary_alt:farm_name.
The ANOVA table is
| Chisq | Df | Pr(>Chisq) | |
|---|---|---|---|
| farm_type | 1.693 | 1 | 0.193 |
| boundary_alt | 4.003 | 3 | 0.261 |
| season | 29.422 | 2 | 0.000 |
| farm_type:boundary_alt | 5.964 | 3 | 0.113 |
| farm_type:season | 0.058 | 2 | 0.971 |
| boundary_alt:season | 8.180 | 6 | 0.225 |
| farm_type:boundary_alt:season | 10.923 | 6 | 0.091 |
The main effect for season is the only significant term.
We fit a negative binomial generalised linear mixed model. The log link function is used. The model has the three-way interaction of farm_type, boundary_alt and season. There is a random effect for boundary_alt:farm_name.
The ANOVA table is
| Chisq | Df | Pr(>Chisq) | |
|---|---|---|---|
| farm_type | 2.347 | 1 | 0.126 |
| boundary_alt | 1.195 | 3 | 0.754 |
| season | 36.430 | 2 | 0.000 |
| farm_type:boundary_alt | 0.915 | 3 | 0.822 |
| farm_type:season | 0.506 | 2 | 0.777 |
| boundary_alt:season | 11.071 | 6 | 0.086 |
| farm_type:boundary_alt:season | 4.278 | 6 | 0.639 |
The main effect for season is the only significant term.
We fit a negative binomial generalised linear mixed model. The log link function is used. The model has farm_type, boundary_alt and season plus all the two-interactions of these three terms. The model failed to converge with the three-way interaction so it was removed. There is a random effect for boundary_alt:farm_name.
The ANOVA table is
| Chisq | Df | Pr(>Chisq) | |
|---|---|---|---|
| farm_type | 4.841 | 1 | 0.028 |
| boundary_alt | 4.549 | 3 | 0.208 |
| season | 34.651 | 2 | 0.000 |
| farm_type:boundary_alt | 0.844 | 3 | 0.839 |
| farm_type:season | 1.349 | 2 | 0.509 |
| boundary_alt:season | 9.202 | 6 | 0.163 |
The main effects for season and farm_type are significant.
We fit a negative binomial generalised linear mixed model. The log link function is used. The model has the main-effect for farm_type, boundary_alt and season. The interaction terms caused convergence problems (or were not significant). There is a random effect for boundary_alt:farm_name.
The ANOVA table is
| Chisq | Df | Pr(>Chisq) | |
|---|---|---|---|
| farm_type | 10.649 | 1 | 0.001 |
| boundary_alt | 12.190 | 3 | 0.007 |
| season | 12.418 | 2 | 0.002 |
The main effects are all significant.